Finding the Area of Circles and Their Segments

The video tutorial covers lesson 8.3 on the area of circles. It begins with an introduction to the formula for calculating the area of a circle, which is pi times the radius squared. The tutorial provides several examples, including calculations using both radius and diameter, and emphasizes the importance of using the correct formula. It also includes review questions and exercises on semicircles and advanced problems involving circle sections. The lesson concludes with a summary of the key points covered.

What is the formula to calculate the area of a circle?

• pi * diameter

• pi * diameter / 2

• pi * radius * radius

• 2 * pi * radius

How would you calculate the area of a circle if only the radius is given?

• Square the radius and multiply by pi

• Multiply the radius by 2 and then by pi

• Divide the radius by 2 and multiply by pi

• Square the radius and divide by pi

If the diameter of a circle is 14 cm, what is the radius?

• 7 cm

• 28 cm

• 14 cm

• 3.5 cm

What is the area of a circle with a radius of 7 using pi as 3.14?

• 157 cm²

• 153.86 cm²

• 150 cm²

• 154 cm²

How do you calculate the area of a circle when given the diameter?

• Multiply the diameter by 2 and use it as the radius

• Square the diameter and multiply by pi

• Divide the diameter by 2 and use it as the radius

• Use the diameter directly in the area formula

For a tire with a known diameter, what geometric measure is essential for calculating the rotation distance?

• Volume

• Radius

• Circumference

• Area

How do you find the area of a semicircle with a diameter of 30 feet?

• 2 * pi * 15

• pi * 15 * 15

• pi * 30 * 30

• pi * 15 * 15 / 2

What is the correct way to calculate the area of a semicircle?

• Divide the diameter by 2, square it, and multiply by pi

• Multiply pi by the square of the diameter

• Multiply pi by the square of the radius and then divide by 2

• Multiply pi by the square of the radius and then divide by 4

What is the area of a quarter circle with a radius of 3 inches?

• 21.195 inches²

• 14.13 inches²

• 28.26 inches²

• 7.065 inches²

If a full circle has an area of 28.26 inches², what is the area of the non-yellow portion if the yellow part is one-fourth?

• 21.195 inches²

• 7.065 inches²

• 14.13 inches²

• 28.26 inches²